> This is a nice solution, and impressive to be found by AI, although the proof is (in hindsight) very simple, and the surprising thing is that Erdos missed it. But there is definitely precedent for Erdos missing easy solutions!
> Also this is not the problem as posed in that paper
> That paper asks a harder version of this problem. The problem which has been solved was asked by Erdos in a couple of later papers.
> One also needs to be careful about saying things like 'open for 30 years'. This does not mean it has resisted 30 years of efforts to solve it! Many Erdos problems (including this one) have just been forgotten about it, and nobody has seriously tried to solve it.[1]
And, indeed, Boris Alexeev (who ran the problem) agrees:
> My summary is that Aristotle solved "a" version of this problem (indeed, with an olympiad-style proof), but not "the" version.
> I agree that the [BEGL96] problem is still open (for now!), and your plan to keep this problem open by changing the statement is reasonable. Alternatively, one could add another problem and link them. I have no preference.[2]
Not to rain on the parade out of spite, it's just that this is neat, but not like, unusually neat compared to the last few months.
[1] https://twitter.com/thomasfbloom/status/1995083348201586965
[2] https://www.erdosproblems.com/forum/thread/124#post-1899
"I also wonder whether this 'easy' version of the problem has actually appeared in some mathematical competition before now, which would of course pollute the training data if Aristotle [Ed.: the clanker's name] had seen this solution already written up somewhere."